Single- and few-layer transition-metal dichalcogenide nanosheets, such as WSe₂ , TaS₂, and TaSe₂, are prepared by mechanical exfoliation. A Raman microscope is employed to characterize the single-layer (1L) to quinary-layer (5L) WSe₂ nanosheets and WSe₂ single crystals with a laser excitation power ranging from 20 μW to 5.1 mW. Typical first-order together with some second-order and combinational Raman modes are observed. A new peak at around 308 cm⁻¹ is observed in WSe₂ except for the 1L WSe₂, which might arise from interlayer interactions. Red shifting of the A(1g) mode and the Raman peak around 308 cm⁻¹ is observed from 1L to 5L WSe₂. Interestingly, hexagonal- and monoclinic-structured WO₃ thin films are obtained during the local oxidation of thinner (1L-3L) and thicker (4L and 5L) WSe₂ nanosheets, while laser-burned holes are found during the local oxidation of the WSe₂ single crystal. In addition, the characterization of TaS₂ and TaSe₂ thin layers is also conducted.